How to set up shape key driver in 2.80?
The problem was that I was setting a driver for the MUTE property of the shape key, not the VALUE property. In order to set a driver for the VALUE, right click the value and you will see an option to add a driver.

I was convinced yesterday that it was not possible to right-click the VALUE (as of 2.80) and see an option to add a driver, that I had to right-click the checkbox instead. This was a mistake. Thank you to everyone (@Edgel3D) who tried to help. The problem is now solved.